GT Vol 1 (1997) Paper 6 (Abstract)

Geometry & Topology, Vol. 1 (1997) Paper no. 6, pages 71-89.

An invariant of smooth 4-manifolds

Laurence R Taylor

Abstract. We define a diffeomorphism invariant of smooth 4-manifolds which we can estimate for many smoothings of R^4 and other smooth 4-manifolds. Using this invariant we can show that uncountably many smoothings of R^4 support no Stein structure. (Gompf has constructed uncountably many smoothings of R^4 which do support Stein structures.) Other applications of this invariant are given.

Keywords. Smooth 4-manifolds, Stein manifolds, covering spaces

AMS subject classification. Primary: 57R10. Secondary: 57N13.

DOI: 10.2140/gt.1997.1.71

E-print: arXiv:math.GT/9712292

Submitted to GT on October 21, 1997. Paper accepted November 24, 1997.

PostScript file (280 KB)
Compressed PostScript file (108 KB)
PDF file with embedded fonts (213 KB)
PDF file without embedded fonts (143 KB)
Reprint cover (45 KB PS file)

Notes on file formats

Laurence R Taylor
Department of Mathematics
University of Notre Dame
Notre Dame, IN 46556
USA
Email: taylor.2@nd.edu

GT home page

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to http://msp.warwick.ac.uk/.